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Here's one of the Census tables referenced in the article I mentioned above. It's in two parts, it seemed to be a bit too wide to fit as one part. I believe that it lacks the data to draw any conclusions vis-a-vis family status and crime.

I did include a couple of comments from the Census Bureau pdf file about family disorder but I don't this study talks about its impact on crime.

America’s Families and Living Arrangements: 2012

http://www.census.gov/prod/2013pubs/p20-570.pdf

PART 1 of 2

Family Groups.

Households can contain
- more than one married-couple family
- or one-parent family;
Nonfamily households can contain
- families that are not related to the householder.

In 1970 the Census Bureau developed the concept of the family group to count all of these types of families.

Family groups include

family households plus
all family groups that do not include the householder;
- these subfamilies may consist of either
  - married couples or
  - parent-child units;
- an individual may be counted in two different family groups; for example,
  - the householder and her adult daughter and granddaughter form one family group;
  - the adult daughter and her child form a second family group, a mother-child subfamily.

Reference people are

the members of a household around whom family units are organized;
in family households
- the householder is always the reference person for the primary family, while
- another member of the household would be the reference person for the subfamily.

Households. A household

contains one or more people;
everyone living in a housing unit makes up a household;
one of the people who owns or rents the residence is designated as the householder.

For the purposes of examining family and household composition two types of households are defined:

family
- at least two members related by
- birth,
- marriage, or
- adoption
- one of whom is the householder
nonfamily
- a person living alone or
- a householder who shares the housing unit only with nonrelatives — for example,
  - boarders or
  - roommates;
- the nonrelatives of the householder may be related to each other.

Family households are maintained by

married couples or
by a man or woman living with other relatives
children may or may not be present.

In contrast, nonfamily households are maintained only by

men or
women

with no relatives at home.

Own children are a subset of all children — they are the

biological,
step, or
adopted child

of the

householder or
family reference person (in the case of subfamilies)

for the universe being considered, whether

household,
family, or
family group.

Own children are also limited to

children who have never been married,
are under the age of 18 (unless otherwise specified), and
are not themselves a family reference person.

Foster children are not included as own children since they are not related to the householder.

Black children (55 percent) and Hispanic children (31 percent) were more likely to live with one parent than non-Hispanic White children (21 percent) or Asian children (13 percent) . . . In 2011, married-couple households made up 81 percent of the family households that an Asian householder maintained and 80 percent that a White, non-Hispanic householder maintained. The corresponding proportion among Hispanic and Black householders was smaller: 62 percent and 44 percent, respectively. Likewise, other family households were more common among Hispanic or Black householders than they were among Asian or non-Hispanic White householders

Table 1. Households by Type and Selected Characteristics: ACS 2011

	All households		Family households
					Other	families
Characteristic	Number	Margin of error¹	Total	Married couple	Male house-holder	Female house-holder
All households	114,991,725	179,541	76,084,006	55,519,648	5,457,141	15,107,217
Age of Householder
15 to 24 years	4,704,541	44,095	2,058,709	791,259	386,058	881,392
25 to 34 years	17,704,876	60,479	11,834,989	7,547,784	1,145,249	3,141,956
35 to 44 years	21,065,572	48,364	16,560,256	11,440,262	1,321,452	3,798,542
45 to 54 years	. 24,351,960	50,700	17,651,283	13,008,878	1,308,663	3,333,742
55 to 64 years	21,760,211	51,095	14,293,163	11,643,837	731,021	1,918,305
65 years and over	25,404,565	61,226	13,685,606	11,087,628	564,698	2,033,280
Race and Hispanic Origin of Householder
White alone	89,716,881	118,696	58,946,781	45,982,567	3,802,675	9,161,539
Non-Hispanic	80,686,965	98,050	51,980,137	41,500,162	3,060,572	7,419,403
Black or African American alone	13,879,391	46,747	8,726,419	3,804,021	836,460	4,085,938
American Indian and Alaska Native alone	814,468	15,555	557,425	315,753	61,588	180,084
Asian alone	4,644,197	24,448	3,446,258	2,787,491	219,358	439,409
Native Hawaiian and Other Pacific Islander alone	130,399	4,921	100,674	67,105	11,180	22,389
Some Other Race alone	3,841,498	29,836	3,026,253	1,759,462	404,534	862,257
Two or More Races	1,964,891	34,711	1,280,196	803,249	121,346	355,601
Hispanic (any race)	13,637,150	56,416	10,541,142	6,528,120	1,212,573	2,800,449
Size of Household
1 person	31,886,794	114,173	X	X	X	X
2 people	38,635,170	115,300	32,882,461	24,712,814	2,171,427	5,998,220
3 people	18,044,529	75,552	17,225,354	11,006,882	1,611,009	4,607,463
4 people	15,030,350	58,958	14,710,713	11,290,906	903,885	2,515,922
5 people	6,940,508	46,062	6,854,293	5,268,439	440,483	1,145,371
6 people	2,704,873	26,971	2,674,980	2,003,798	186,396	484,786
7 or more people	1,749,501	22,103	1,736,205	1,236,809	143,941	355,455
Average size	2.64	Z	3.34	3.28	3.50	3.49
Number of Related Children Under 18
No related children	77,844,222	158,791	38,936,503	31,462,882	2,372,577	5,101,044
With related children²	37,147,503	78,916	37,147,503	24,056,766	3,084,564	10,006,173
1 child	15,902,634	66,375	15,902,634	9,325,508	1,714,744	4,862,382
2 children	13,414,048	58,604	13,414,048	9,368,291	889,656	3,156,101
3 children	5,430,075	38,142	5,430,075	3,774,744	334,647	1,320,684
4 or more children	2,400,746	27,581	2,400,746	1,588,223	145,517	667,006
Presence of Own Children Under 18
No own children	81,228,585	150,547	42,320,866	32,958,335	2,805,085	6,557,446
With own children ²	33,763,140	78,715	33,763,140	22,561,313	2,652,056	8,549,771
With own children under 12	24,346,074	69,573	24,346,074	16,523,483	1,854,578	5,968,013
With own children under 6	14,307,333	64,326	14,307,333	9,855,286	1,117,335	3,334,712
With own children under 3	8,086,757	60,155	8,086,757	5,697,549	644,262	1,744,946
With own children under 1	2,782,662	28,518	2,782,662	1,984,657	242,226	555,779
Tenure
Owned home	74,264,435	230,440	54,627,945	44,808,444	2,929,038	6,890,463
Rented home	38,515,453	103,548	20,313,830	10,027,501	2,405,146	7,881,183
Occupied without payment	2,211,837	24,889	1,142,231	683,703	122,957	335,571

America’s Families and Living Arrangements: 2012

http://www.census.gov/prod/2013pubs/p20-570.pdf

PART 2 of 2. See PART 1 for definitions.

Table 1. Households by Type and Selected Characteristics: ACS 2011

	Nonfamily households
Characteristic	Total	Male house-holder	Female house-holder
All households	38,907,719	18,030,888	20,876,831
Age of Householder
15 to 24 years	2,645,832	1,311,058	1,334,774
25 to 34 years	5,869,887	3,434,054	2,435,833
35 to 44 years	4,505,316	2,801,769	1,703,547
45 to 54 years	. 6,700,677	3,617,182	3,083,495
55 to 64 years	7,467,048	3,333,840	4,133,208
65 years and over	11,718,959	3,532,985	8,185,974
Race and Hispanic Origin of Householder
White alone	30,770,100	14,173,114	16,596,986
Non-Hispanic	28,706,828	13,082,329	15,624,499
Black or African American alone	5,152,972	2,312,473	2,840,499
American Indian and Alaska Native alone	257,043	133,593	123,450
Asian alone	1,197,939	591,684	606,255
Native Hawaiian and Other Pacific Islander alone	29,725	15,795	13,930
Some Other Race alone	815,245	472,839	342,406
Two or More Races	684,695	331,390	353,305
Hispanic (any race)	3,096,008	1,673,986	1,422,022
Size of Household
1 person	31,886,794	14,119,225	17,767,569
2 people	5,752,709	3,069,470	2,683,239
3 people	819,175	533,053	286,122
4 people	319,637	218,093	101,544
5 people	86,215	59,209	27,006
6 people	29,893	22,465	7,428
7 or more people	13,296	9,373	3,923
Average size	1.28	1.35	1.22
Number of Related Children Under 18
No related children	38,907,719	18,030,888	20,876,831
With related children²	X	X	X
1 child	X	X	X
2 children	X	X	X
3 children	X	X	X
4 or more children	X	X	X
Presence of Own Children Under 18
No own children	38,907,719	18,030,888	20,876,831
With own children ²	X	X	X
With own children under 12	X	X	X
With own children under 6	X	X	X
With own children under 3	X	X	X
With own children under 1	X	X	X
Tenure
Owned home	19,636,490	8,511,414	11,125,076
Rented home	18,201,623	8,972,270	9,229,353
Occupied without payment	1,069,606	547,204	522,402

X Not applicable.

Z Rounds to zero.

¹This number, when added to or subtracted from the estimated total number of households in each category or the average household size, represents the 90 percent confidence interval around the estimate.

²Excludes ever-married children under 18 years.

Note: See for further information on the accuracy of the data.

Source: U.S.Census Bureau, American Community Survey, 2011